Vector Calculus

[APK911]

As a large wheel rolls along the x-axis, the point Q at the center of the wheel will move horizontally. P is a point on the rim of the wheel and initially, i.e, when t=0, point P lies at the origin. Suppose that the forward speed and the radius of the wheel are such that the velocity of P at time t seconds later is v m/s where, v=(1-cos(t))i+sin(t)j. Find the diameter of the wheel.

Sorry, the question is a little long... But in order to find the diameter, would I have to find the position vector at time t, then sub in t as 2pi, and get the magnitude of the vector?

I've also attached a photo of the question and diagram, if that helps...

[Eric11267]

As a large wheel rolls along the x-axis, the point Q at the center of the wheel will move horizontally. P is a point on the rim of the wheel and initially, i.e, when t=0, point P lies at the origin. Suppose that the forward speed and the radius of the wheel are such that the velocity of P at time t seconds later is v m/s where, v=(1-cos(t))i+sin(t)j. Find the diameter of the wheel.

Sorry, the question is a little long... But in order to find the diameter, would I have to find the position vector at time t, then sub in t as 2pi, and get the magnitude of the vector?

I've also attached a photo of the question and diagram, if that helps...

I think you need to find the position vector and then find the maximum value of the vertical component. That way you'll have the highest distance above the x axis that P is, which would give you the diameter. Though I might be wrong

[APK911]

Oh, actually that makes sense. Thank you very much!